On the balancing property of Matkowski means
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DOI: 10.1007/s00010-020-00758-7
Abstract: Let $$I\subseteq \mathbb {R}$$ I ⊆ R be a nonempty open subinterval. We say that a two-variable mean $$M:I\times I\rightarrow \mathbb {R}$$ M : I × I → R enjoys the balancing property if, for… read more here.
Keywords: arithmetic means; quasi arithmetic; matkowski means; balancing property ... See more keywords
Preserver Problems Related to Quasi-Arithmetic Means of Invertible Positive Operators
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DOI: 10.1007/s00020-018-2426-x
Abstract: In this paper we mainly discuss different preserver problems on the cone of positive definite matrices which are related to certain quasi-arithmetic means. read more here.
Keywords: quasi arithmetic; related quasi; preserver problems; arithmetic means ... See more keywords
On a lattice-like property of quasi-arithmetic means
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.123892
Abstract: We will prove that in a family of quasi-arithmetic means sattisfying certain smoothness assumption (embed with a naural pointwise ordering) every finite family has both supremum and infimum, which is also a quasi-arithmetic mean sattisfying… read more here.
Keywords: quasi arithmetic; property quasi; like property; lattice like ... See more keywords
Convexity according to a pair of quasi-arithmetic means and inequalities
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DOI: 10.1016/j.jmaa.2020.124059
Abstract: Abstract We consider a class of generalized convex functions, which are defined according to a pair of quasi-arithmetic means and called ( M ϕ , M ψ ) -convex functions, and establish various Fejer type… read more here.
Keywords: arithmetic means; pair quasi; according pair; quasi arithmetic ... See more keywords
Generalizing the Alpha-Divergences and the Oriented Kullback-Leibler Divergences with Quasi-Arithmetic Means
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DOI: 10.3390/a15110435
Abstract: The family of α-divergences including the oriented forward and reverse Kullback–Leibler divergences is often used in signal processing, pattern recognition, and machine learning, among others. Choosing a suitable α-divergence can either be done beforehand according… read more here.
Keywords: arithmetic means; quasi arithmetic; leibler divergences; divergence ... See more keywords
Stochastic Order and Generalized Weighted Mean Invariance
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DOI: 10.3390/e23060662
Abstract: In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from… read more here.
Keywords: mean; quasi arithmetic; invariance; order ... See more keywords
Quasi-Arithmetic Type Mean Generated by the Generalized Choquet Integral
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DOI: 10.3390/sym12122104
Abstract: It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and… read more here.
Keywords: quasi arithmetic; mean; choquet integral; generalized choquet ... See more keywords
An interpolation of Jensen's inequality and its converses with applications to quasi-arithmetic mean inequalities
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Inequalities"
DOI: 10.7153/jmi-2019-13-08
Abstract: In this paper, we show an interpolation of Davis-Choi-Jensen operator inequality and the converse inequality for Hilbert space operators. As applications, we obtain an interpolation of quasi-arithmetic mean inequalities and the converse inequalities. read more here.
Keywords: inequality; inequalities interpolation; mean inequalities; arithmetic mean ... See more keywords